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In the not so unlikely scenario of total compromise of computers accessible to a group of users, they might be tempted to resort to human-computable paper-and-pencil cryptographic methods aided by a classic Tabula Recta, which helps to perform addition and subtraction directly with letters. But do these classic algorithms, or some new ones using the same simple tools, have any chance against computer-aided cryptanalysis? In this paper I discuss how some human-computable algorithms can indeed afford sufficient security in this situation, drawing conclusions from computer-based statistical analysis. Three kinds of algorithms are discussed: those that concentrate entropy from shared text sources, stream ciphers based on arithmetic of non-binary spaces, and hash-like algorithms that may be used to generate a password from a challenge text.

In this work we make us of Livens principle (sometimes also referred to as Hamilton-Pontryagin principle) in order to obtain a novel structure-preserving integrator for mechanical systems. In contrast to the canonical Hamiltonian equations of motion, the Euler-Lagrange equations pertaining to Livens principle circumvent the need to invert the mass matrix. This is an essential advantage with respect to singular mass matrices, which can yield severe difficulties for the modelling and simulation of multibody systems. Moreover, Livens principle unifies both Lagrangian and Hamiltonian viewpoints on mechanics. Additionally, the present framework avoids the need to set up the system's Hamiltonian. The novel scheme algorithmically conserves a general energy function and aims at the preservation of momentum maps corresponding to symmetries of the system. We present an extension to mechanical systems subject to holonomic constraints. The performance of the newly devised method is studied in representative examples.

Artificial Neural Networks (ANN) have gained large popularity thanks to their ability to learn using the well-known backpropagation algorithm. On the other hand, Spiking Neural Networks (SNNs), despite having wider abilities than ANNs, have always presented a challenge in the training phase. This paper shows a new method to perform supervised learning on SNNs, using Spike Timing Dependent Plasticity (STDP) and homeostasis, aiming at training the network to identify spatial patterns. The method is tested using the SpiNNaker digital architecture. A SNN is trained to recognise one or multiple patterns and performance metrics are extracted to measure the performance of the network. Some considerations are drawn from the results showing that, in the case of a single trained pattern, the network behaves as the ideal detector, with 100% accuracy in detecting the trained pattern. However, as the number of trained patterns on a single network increases, the accuracy of the identification is linked to the similarities between these patterns. This method of training an SNN to detect spatial patterns may be applied on pattern recognition in static images or traffic analysis in computer networks, where each network packet represents a spatial pattern. It will be stipulated that the homeostatic factor may enable the network to detect patterns with some degree of similarities, rather than only perfectly matching patterns.

In the realm of machine learning, the data may contain additional attributes, known as privileged information (PI). The main purpose of PI is to assist in the training of the model and then utilize the acquired knowledge to make predictions for unseen samples. Support vector regression (SVR) is an effective regression model, however, it has a low learning speed due to solving a convex quadratic problem (QP) subject to a pair of constraints. In contrast, twin support vector regression (TSVR) is more efficient than SVR as it solves two QPs each subject to one set of constraints. However, TSVR and its variants are trained only on regular features and do not use privileged features for training. To fill this gap, we introduce a fusion of TSVR with learning using privileged information (LUPI) and propose a novel approach called twin support vector regression with privileged information (TSVR+). The regularization terms in the proposed TSVR+ capture the essence of statistical learning theory and implement the structural risk minimization principle. We use the successive overrelaxation (SOR) technique to solve the optimization problem of the proposed TSVR+, which enhances the training efficiency. As far as our knowledge extends, the integration of the LUPI concept into twin variants of regression models is a novel advancement. The numerical experiments conducted on UCI, stock and time series data collectively demonstrate the superiority of the proposed model.

We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic array. Under the same umbrella, FFT-PIM allows computing the potential for 1D, 2D, and 3D periodicities for dynamic and static problems, including problems with and without a periodic phase shift. The computational complexity of the FFT-PIM is of $O(N \log N)$ for $N$ spatially coinciding sources and observer points. The FFT-PIM uses rapidly converging series representations of the Green's function serving as a kernel in the superposition sum. Based on these representations, the FFT-PIM splits the potential into its near-zone component, which includes a small number of images surrounding the unit cell of interest, and far-zone component, which includes the rest of an infinite number of images. The far-zone component is evaluated by projecting the non-uniform sources onto a sparse uniform grid, performing superposition sums on this sparse grid, and interpolating the potential from the uniform grid to the non-uniform observation points. The near-zone component is evaluated using an FFT-based method, which is adapted to efficiently handle non-uniform source-observer distributions within the periodic unit cell. The FFT-PIM can be used for a broad range of applications, such as periodic problems involving integral equations in computational electromagnetic and acoustic, micromagnetic solvers, and density functional theory solvers.

Representations from transformer-based unidirectional language models are known to be effective at predicting brain responses to natural language. However, most studies comparing language models to brains have used GPT-2 or similarly sized language models. Here we tested whether larger open-source models such as those from the OPT and LLaMA families are better at predicting brain responses recorded using fMRI. Mirroring scaling results from other contexts, we found that brain prediction performance scales logarithmically with model size from 125M to 30B parameter models, with ~15% increased encoding performance as measured by correlation with a held-out test set across 3 subjects. Similar logarithmic behavior was observed when scaling the size of the fMRI training set. We also characterized scaling for acoustic encoding models that use HuBERT, WavLM, and Whisper, and we found comparable improvements with model size. A noise ceiling analysis of these large, high-performance encoding models showed that performance is nearing the theoretical maximum for brain areas such as the precuneus and higher auditory cortex. These results suggest that increasing scale in both models and data will yield incredibly effective models of language processing in the brain, enabling better scientific understanding as well as applications such as decoding.

Recent advances in deep learning have given us some very promising results on the generalization ability of deep neural networks, however literature still lacks a comprehensive theory explaining why heavily over-parametrized models are able to generalize well while fitting the training data. In this paper we propose a PAC type bound on the generalization error of feedforward ReLU networks via estimating the Rademacher complexity of the set of networks available from an initial parameter vector via gradient descent. The key idea is to bound the sensitivity of the network's gradient to perturbation of the input data along the optimization trajectory. The obtained bound does not explicitly depend on the depth of the network. Our results are experimentally verified on the MNIST and CIFAR-10 datasets.

In many applications, it is desired to obtain extreme eigenvalues and eigenvectors of large Hermitian matrices by efficient and compact algorithms. In particular, orthogonalization-free methods are preferred for large-scale problems for finding eigenspaces of extreme eigenvalues without explicitly computing orthogonal vectors in each iteration. For the top $p$ eigenvalues, the simplest orthogonalization-free method is to find the best rank-$p$ approximation to a positive semi-definite Hermitian matrix by algorithms solving the unconstrained Burer-Monteiro formulation. We show that the nonlinear conjugate gradient method for the unconstrained Burer-Monteiro formulation is equivalent to a Riemannian conjugate gradient method on a quotient manifold with the Bures-Wasserstein metric, thus its global convergence to a stationary point can be proven. Numerical tests suggest that it is efficient for computing the largest $k$ eigenvalues for large-scale matrices if the largest $k$ eigenvalues are nearly distributed uniformly.

AI research is increasingly industry-driven, making it crucial to understand company contributions to this field. We compare leading AI companies by research publications, citations, size of training runs, and contributions to algorithmic innovations. Our analysis reveals the substantial role played by Google, OpenAI and Meta. We find that these three companies have been responsible for some of the largest training runs, developed a large fraction of the algorithmic innovations that underpin large language models, and led in various metrics of citation impact. In contrast, leading Chinese companies such as Tencent and Baidu had a lower impact on many of these metrics compared to US counterparts. We observe many industry labs are pursuing large training runs, and that training runs from relative newcomers -- such as OpenAI and Anthropic -- have matched or surpassed those of long-standing incumbents such as Google. The data reveals a diverse ecosystem of companies steering AI progress, though US labs such as Google, OpenAI and Meta lead across critical metrics.

Deep learning constitutes a recent, modern technique for image processing and data analysis, with promising results and large potential. As deep learning has been successfully applied in various domains, it has recently entered also the domain of agriculture. In this paper, we perform a survey of 40 research efforts that employ deep learning techniques, applied to various agricultural and food production challenges. We examine the particular agricultural problems under study, the specific models and frameworks employed, the sources, nature and pre-processing of data used, and the overall performance achieved according to the metrics used at each work under study. Moreover, we study comparisons of deep learning with other existing popular techniques, in respect to differences in classification or regression performance. Our findings indicate that deep learning provides high accuracy, outperforming existing commonly used image processing techniques.